CHE 341-Process Control

Spring 2005, 03/11/2005

Project

Modified from Exercise-IV in Doyle F.J by Pinar Baycili under guidance of Prof.A.Linninger

 

 

SECOND-ORDER DYNAMIC SYSTEM ANALYSIS

 

Objective

 

The purpose of this project is to understand the dynamic properties of a second-order system for various values of the system gain, period, and damping coefficient and to observe the dynamic response to different input signals.

 

Introduction:

 

The dynamic behavior of a second-order system is determined by the gain, the time constant, and the damping coefficient. The second-order system transfer function is as follows:

G(s) is the transfer function;

Kp is the system gain;

τp is the natural period of the system;

ζ is the damping coefficient

 

 

Problems

 

1)      Set the system gain (Kp) to 10.0 the value of A to 40.0, and the value of B to 14.0. Now set the initial value of the Step Function to 0.0 and the final value of the Step Function to 1.0.

 

Is the system overdamped, underdamped or critically damped?

 

If the system is underdamped, what is the overshoot decay ratio, rise time, settling time and the period of oscillation?

 

2)      Set the system gain (Kp) to 10.0 the value of A to 18.0, and the value of B to 2.0. Repeat the simulation for the same step function in the first question.

     

Is the system overdamped, underdamped or critically damped?

 

If the system is underdamped, what is the overshoot decay ratio, rise time, settling time and the period of oscillation?

 

3)      Set the system gain (Kp) to 10.0 the value of A to 40.0, and the value of B to 14.0.

      Repeat the simulation for the same step function in the first question.

 

      Is the system overdamped, underdamped or critically damped?

 

If the system is underdamped, what is the overshoot decay ratio, rise time, settling time and the period of oscillation?

 

4)   Plot the Bode diagrams for systems given in the questions 1, 2 and 3. Determine the

      gain margin and the phase margin using these diagrams.

 

5)   Discuss whether the systems given in the questions 1, 2 and 3 are stable.

 

6)   System Identification Problem:

 

From your graphs, read the period and overshoot. Using these values, calculate the damping coefficient and the time constant of the system. Compare these results with the given values.

 

- Discuss all your results from (1) – (6) in a report.